Let \(A=\begin{pmatrix} 4 & 1 \\ -9 &-2 \end{pmatrix}.\) If \(A^{100}\) can be represented as \(A^{100}=\begin{pmatrix} a & b \\ c & d \end{pmatrix},\) what is the value of \(a+b+c+d?\)

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